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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 649318, 7 pages
Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow
1School of Highway, Chang’an University, Xi’an 710064, China
2School of Science, Guangxi University for Nationalities, Nanning 530006, China
3College of Instrumentation & Electrical Engineering, Jilin University, Changchun 130061, China
Received 10 May 2014; Accepted 20 May 2014; Published 29 June 2014
Academic Editor: Xiao-Jun Yang
Copyright © 2014 Yang Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- V. E. Tarasov, “Wave equation for fractal solid string,” Modern Physics Letters B, vol. 19, no. 15, pp. 721–728, 2005.
- S. Momani and Z. Odibat, “Analytical approach to linear fractional partial differential equations arising in fluid mechanics,” Physics Letters A: General, Atomic and Solid State Physics, vol. 355, no. 4-5, pp. 271–279, 2006.
- S. Momani and Z. Odibat, “Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method,” Applied Mathematics and Computation, vol. 177, no. 2, pp. 488–494, 2006.
- Y. Z. Povstenko, “Fractional heat conduction equation and associated thermal stress,” Journal of Thermal Stresses, vol. 28, no. 1, pp. 83–102, 2005.
- L. Vázquez, J. J. Trujillo, and M. P. Velasco, “Fractional heat equation and the second law of thermodynamics,” Fractional Calculus and Applied Analysis, vol. 14, no. 3, pp. 334–342, 2011.
- E. Lutz, “Fractional transport equations for Lévy stable processes,” Physical Review Letters, vol. 86, no. 11, pp. 2208–2211, 2001.
- A. Kadem, Y. Luchko, and D. Baleanu, “Spectral method for solution of the fractional transport equation,” Reports on Mathematical Physics, vol. 66, no. 1, pp. 103–115, 2010.
- N. Laskin, “Fractional Schrödinger equation,” Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, vol. 66, no. 5, Article ID 056108, 7 pages, 2002.
- S. I. Muslih, O. P. Agrawal, and D. Baleanu, “A fractional Schrödinger equation and its solution,” International Journal of Theoretical Physics, vol. 49, no. 8, pp. 1746–1752, 2010.
- D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, vol. 3 of Complexity, Nonlinearity and Chaos, World Scientific, Boston, Mass, USA, 2012.
- H. Jafari and S. Seifi, “Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 2006–2012, 2009.
- H. Jafari, H. Tajadodi, N. Kadkhoda, and D. Baleanu, “Fractional subequation method for Cahn-Hilliard and Klein-Gordon equations,” Abstract and Applied Analysis, vol. 2013, Article ID 587179, 5 pages, 2013.
- J. Hristov, “Heat-balance integral to fractional (half-time) heat diffusion sub-model,” Thermal Science, vol. 14, no. 2, pp. 291–316, 2010.
- J. Hristov, “Transient flow of a generalized second grade fluid due to a constant surface shear stress: an approximate integral-balance solution,” International Review of Chemical Engineering, vol. 3, no. 6, pp. 802–809, 2011.
- A. H. Bhrawy and M. A. Alghamdi, “A shifted Jacobi-Gauss-Lobatto collocation method for solving nonlinear fractional Langevin equation involving two fractional orders in different intervals,” Boundary Value Problems, vol. 2012, article 62, 2012.
- A. H. Bhrawy and M. M. Al-Shomrani, “A shifted Legendre spectral method for fractional-order multi-point boundary value problems,” Advances in Difference Equations, vol. 2012, article 8, 2012.
- A. H. Bhrawy and D. Baleanu, “A spectral Legendre-Gauss-Lobatto collocation method for a space-fractional advection diffusion equations with variable coefficients,” Reports on Mathematical Physics, vol. 72, no. 2, pp. 219–233, 2013.
- A. Atangana and D. Baleanu, “Numerical solution of a kind of fractional parabolic equations via two difference schemes,” Abstract and Applied Analysis, vol. 2013, Article ID 828764, 8 pages, 2013.
- X.-J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science, New York, NY, USA, 2012.
- X.-J. Yang, H. M. Srivastava, J.-H. He, and D. Baleanu, “Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives,” Physics Letters A, vol. 377, no. 28–30, pp. 1696–1700, 2013.
- Y. Zhao, D. Baleanu, C. Cattani, D.-F. Cheng, and X.-J. Yang, “Maxwell's equations on Cantor sets: a local fractional approach,” Advances in High Energy Physics, vol. 2013, Article ID 686371, 6 pages, 2013.
- X.-J. Yang and D. Baleanu, “Fractal heat conduction problem solved by local fractional variation iteration method,” Thermal Science, vol. 17, no. 2, pp. 625–628, 2013.
- C. F. Liu, S. S. Kong, and S. J. Yuan, “Reconstructive schemes for variational iteration method within Yang-Laplace transform with application to fractal heat conduction problem,” Thermal Science, vol. 17, no. 3, pp. 715–721, 2013.
- X. J. Yang, D. Baleanu, and J. T. Machado, “Application of the local fractional Fourier series to fractal signals,” in Discontinuity and Complexity in Nonlinear Physical Systems, pp. 63–89, Springer, 2014.
- K. Liu, R.-J. Hu, C. Cattani, G.-N. Xie, X.-J. Yang, and Y. Zhao, “Local fractional -transforms with applications to signals on cantor sets,” Abstract and Applied Analysis, vol. 2014, Article ID 638648, 6 pages, 2014.
- G. Yi, “Local fractional Z transform in fractal space,” Advances in Digital Multimedia, vol. 1, no. 2, pp. 96–102, 2012.
- X.-J. Yang, D. Baleanu, H. M. Srivastava, and J. A. Tenreiro Machado, “On local fractional continuous wavelet transform,” Abstract and Applied Analysis, vol. 2013, Article ID 725416, 5 pages, 2013.
- X.-J. Yang, D. Baleanu, and J. A. Tenreiro Machado, “Systems of Navier-Stokes equations on Cantor sets,” Mathematical Problems in Engineering, vol. 2013, Article ID 769724, 8 pages, 2013.
- X.-J. Yang, D. Baleanu, and J. A. Tenreiro Machado, “Mathematical aspects of Heisenberg uncertainty principle within local fractional Fourier analysis,” Boundary Value Problems, vol. 2013, article 131, 2013.
- C.-Y. Long, Y. Zhao, and H. Jafari, “Mathematical models arising in the fractal forest gap via local fractional calculus,” Abstract and Applied Analysis, vol. 2014, Article ID 782393, 6 pages, 2014.
- L.-F. Wang, X.-J. Yang, D. Baleanu, C. Cattani, and Y. Zhao, “Fractal dynamical model of vehicular traffic flow within the local fractional conservation laws,” Abstract and Applied Analysis, vol. 2014, Article ID 635760, 5 pages, 2014.
- J.-H. He and F.-J. Liu, “Local fractional variational iteration method for fractal heat transfer in silk cocoon hierarchy,” Nonlinear Science Letters A, vol. 4, no. 1, pp. 15–20, 2013.
- A. M. Yang, J. Li, H. M. Srivastava, G. N. Xie, and X. J. Yang, “The local fractional Laplace variational iteration method for solving linear partial differential equations with local fractional derivatives,” Discrete Dynamics in Nature and Society, vol. 2014, Article ID 365981, 2014.
- Y. Z. Zhang, A. M. Yang, and Y. Long, “Initial boundary value problem for fractal heat equation in the semi-infinite region by Yang-Laplace transform,” Thermal Science, 2013.
- C.-G. Zhao, A.-M. Yang, H. Jafari, and A. Haghbin, “The Yang-Laplace transform for solving the IVPs with local fractional derivative,” Abstract and Applied Analysis, vol. 2014, Article ID 386459, 5 pages, 2014.